The oxidation of NO (released in small amounts in the...

The oxidation of $\mathrm{NO}$ (released in small amounts in the exhaust of automobiles) produces the brownish-red gas $\mathrm{NO}_{2},$ which is a component of urban air pollution. $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$$ The rate law for the reaction is rate $=k[\mathrm{NO}]^{2}\left[\mathrm{O}_{2}\right]$ At $25^{\circ} \mathrm{C}, k=7.1 \times 10^{9} \mathrm{~L}^{2} \mathrm{~mol}^{-2} \mathrm{~s}^{-1}$. What would be the rate of the reaction if $[\mathrm{NO}]=0.0010 \mathrm{~mol} \mathrm{~L}^{-1}$ and $\left[\mathrm{O}_{2}\right]=0.034 \mathrm{~mol} \mathrm{I}^{-1}$.

Key Concepts

Reaction Rate

The reaction rate is a measure of how fast reactants are converted into products per unit time. It quantifies the speed of a chemical reaction and can be expressed as the change in concentration of a reactant or product over a set period of time.

Rate Law

The rate law is an equation that relates the reaction rate to the concentrations of reactants, each raised to an exponent that mirrors its order in the reaction. It serves as a mathematical representation of how various reactant concentrations affect the overall reaction rate.

Reaction Order

The reaction order in terms of each reactant is the power to which its concentration is raised in the rate law. The overall order of the reaction is the sum of the orders with respect to all reactants, describing how the rate depends on the concentrations of all the reactants.

Rate Constant

The rate constant, denoted as k in the rate law, is a proportionality factor that is specific to a given reaction at a certain temperature. It provides a measure of the intrinsic speed of the reaction and carries units that depend on the overall order of the reaction.

Dimensional Analysis

Dimensional analysis is used to ensure that the units on both sides of the rate equation are consistent. This involves verifying that the units of the rate constant and reactant concentrations combine appropriately to yield the correct unit for the rate of reaction, typically moles per liter per second.

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